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MathGroup Archive 2006

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Re: Newbie question about column sums of arrays

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68542] Re: [mg68508] Newbie question about column sums of arrays
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Wed, 9 Aug 2006 04:19:26 -0400 (EDT)
  • References: <200608081029.GAA29659@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Aug 8, 2006, at 6:29 AM, George W. Gilchrist wrote:

> I have spent several hours trying to find an answer to what must be
> an incredibly simple problem: how to sum the columns of an array
> containing a random mix of +1 and -1s. For example:
>
> In[7]:=
> AA1=Array[x, {4,4}]/. x:> (-1)^Random[Integer]
>
>
> Out[7]=
> \!\(\*FormBox[
>    RowBox[{"(", "\[NoBreak]", GridBox[{
>          {\(1[1, 1]\), \(1[1, 2]\), \(\((\(-1\))\)[1, 3]\), \(1[1, 4]
> \)},
>          {\(1[2, 1]\), \(1[2, 2]\), \(\((\(-1\))\)[
>            2, 3]\), \(\((\(-1\))\)[2, 4]\)},
>          {\(1[3, 1]\), \(\((\(-1\))\)[3, 2]\), \(1[3, 3]\), \(1[3, 4]
> \)},
>          {\(\((\(-1\))\)[4, 1]\), \(1[4,
>            2]\), \(1[4, 3]\), \(\((\(-1\))\)[4, 4]\)}
>          },
>        RowSpacings->1,
>        ColumnSpacings->1,
>        ColumnAlignments->{Left}], "\[NoBreak]", ")"}],
> TraditionalForm]\)
>
> In[8]:=
> Total[AA1]
>
> Out[8]=
> {(-1)[4,1]+1[1,1]+1[2,1]+1[3,1],
>   (-1)[3,2]+1[1,2]+1[2,2]+1[4,2],
>   (-1)[1,3]+(-1)[2,3]+1[3,3]+1[4,3],
>   (-1)[2,4]+(-1)[4,4]+1[1,4]+1[3,4]}
>
>
> So, Total[] seems to do the right thing, but I cannot get the actual
> sums as real numbers, only this rather verbose representation. I have
> searched the manuals for just about everything I can think of with no
> luck. So, thanks for any help you can give me.

The problem is in your definition of AA1 (incidentally to avoid  
future headaches it helps to use variables that start with lower case  
letters).  Array is meant to take a function as its first argument  
where the arguments to the function are the indices of the array  
element.  It is used for constructing arrays whose element values are  
functions of their position.  The easiest way to make your matrix,  
whose elements do not depend on position is with Table:

In[38]:=
aa1=Table[(-1)^Random[Integer],{4},{4}]
Total[aa1]

Out[38]=
{{-1,-1,1,1},{-1,1,1,-1},{1,-1,1,-1},{-1,1,-1,-1}}

Out[39]=
{-2,0,2,-2}


Regards,

Ssezi

>
>
> Cheers, George
>
> ..................................................................
> George W. Gilchrist                        Email #1: gwgilc at wm.edu
> Department of Biology, Box 8795          Email #2: kitesci at cox.net
> College of William & Mary                    Phone: (757) 221-7751
> Williamsburg, VA 23187-8795                    Fax: (757) 221-6483
> http://gwgilc.people.wm.edu/
>
>


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